Convolutional neural network techniques for the efficient solution of fluid flow in porous media

Resumo

Neural operators, such as Physics-Informed Neural Networks (PINNs), the Fourier Neural Operator (FNO), and the Deep Operator Network (DeepONet), have emerged as promising alternatives to classical numerical methods and modern iterative solvers for addressing dynamic problems involving fluid flow. These neural architectures offer the potential for computational efficiency, improved generalization across varying physical conditions, and the ability to learn mappings directly between functional spaces, reducing the need for pointwise numerical simulations. However, they still fall short of the numerical efficiency achieved by a convolutional neural networks (CNNs) in finite-dimensional tasks. Among CNN variants, U-Net has shown strong performance in solving partial differential equations (PDEs). A key limitation is its reliance on large training datasets, often impractical in reservoir modeling due to limited data availability and proprietary constraints. This study proposes a data augmentation (DA) strategy to enhance U-Net’s generalization and mapping capability. The proposed approach achieved reductions of 64.79% in mean relative error and 84.97% in standard deviation over 10 runs, relative to the U-Net baseline. Moreover, it outperformed DeepONet and FNO on a widely used 2D Darcy benchmark dataset. Inference time was also analyzed, highlighting the potential of the U-Net as a surrogate model for solving thousands of PDEs.